https://doi.org/10.48550/arXiv.2312.12623
Summary
Non-blazar AGN PKS 0521-36 observed over 15 years by Fermi-LAT telescope.
Lomb-Scargle and wavelet analysis reveals three Quasi-periodic oscillations (QPOs).
GP modelling revealed two more QPOs.
Cause of QPOs remains unclear.
Evidence for QPOs seems inconsistent.
Data
ROI is circular region of
\(10^\circ\)
centred at PKS 0521-36
15 years of observations by Fermi-LAT (August 2008 - 2023)
MJD 54683 – 60187 (5504d)
\(\gamma\)
-ray light curve
Uniformly sampled
Method
Compute Lomb-Scargle periodogram.
Compute Weighted wavelet Z-transform.
Fit Gaussian Process model with different kernels
Damped Random Walk,
Simple Harmonic Oscillator, and
Choose best combination using BIC.
Look for “significant” peaks in power.
“Significance” estimation
Results: LSP and WWZ
T = 268, 295, 806 days.
Results: GP Model
Results: GP PSD
Statistical Comments
CARMA is a
stochastic
process not a Gaussian process model.
Computationally heavy, N
\(\approx\)
500
MCMC: 32 chains with 5,000 burn-in + 10,000 steps.
No mention of priors.
The more data you have, the more likely you are to reach significance.
The difference between 3
\(\sigma\)
vs. 5
\(\sigma\)
might not itself be significant.
Note on BIC
\[\textrm{BIC} = -2\mathcal{L} + K \log N\]
BIC should only be used to compare between models that are subsets of eachother.
Not surprising that BIC increases with model complexity.
Manuscript queries
Detected QPOs don’t match between LSP/WWZ and GP models
Used different date ranges MJD 54683 – 60187 (15y) vs. MJD 55358 – 59547 (11.4y) for each.
Kelly et al. (2009) and Li & Wang (2018) are analyses of optical not
\(\gamma\)
-ray light curves.
Where does the “quasi” come from?
LSP and
QPO vs BH Mass